A supermartingale relation for multivariate risk measures |
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| Authors: | Zachary Feinstein Birgit Rudloff |
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| Institution: | 1. Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, 63108 USA.zfeinstein@ese.wustl.edu;3. Institute for Statistics and Mathematics, Vienna University of Economics and Business, Vienna, A-1020 Austria. |
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| Abstract: | The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk measure. Examples of multivariate risk measures satisfying the supermartingale property are given. Crucial for obtaining the results are dual representations of scalarizations of set-valued dynamic risk measures, which are of independent interest in the fast growing literature on multivariate risks. |
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| Keywords: | Set-valued supermartingale Time consistency Dynamic risk measures Transaction costs Set-valued risk measures Multivariate risks |
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